Fully dynamic algorithms for chordal graphs

We present the fist dynamic algorithm to support the following operations on a chordal graph: (1) test whether deleting or inserting an arbitrary edge maintains chordality, (2) delete or insert an arbitrary edge, provided it maintains chordahty. The algorithm also maintains a clique tree of the graph: which provides the graph’s clique number and chromatic number. We give two implementations. In the first, each operation runs in O(n) time, where n is the number of vertices. In the second, testing a deletion runs in O(n) time, testing an insertion runs in O(log* n) time, deleting runs in O(nlog rz) time, and inserting runs in O(n/logn) time. All of these are worst-case times. The algorithm is very simple and uses no complex data structures.

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